That makes the TTS good for a sprint to 62mph in 5.4sec, which you can shave to 5.2sec if you order the car with Audi’s optional S Tronic double clutch paddle shift. The roadster version, despite some extra mass and a shape that's slightly less slippery, will reach 62mph in 5.6sec. All versions are pegged at 155mph.

You can identify a TTS by its prominent, body-coloured front spoiler lip, a metallic grey-finished grille and rear diffuser, Audi’s trademark LED running lights, deeper sills, aluminium capped door mirrors, 18in alloys and a quartet of exhaust pipes from the outside – inside, it gets alcantara/leather seats, more aluminium finishing and grey-faced instruments.

On the mechanical front, magnetic variable rate dampers, with two settings, are standard, and packaged with stiffer springs and anti-roll bars. Otherwise, the TTS is largely stock TT, which means a lightweight bodyshell of aluminium and steel, the steel concentrated at the rear end in the quest for more favourable weight distribution.

The standard 2.0 TT is itself quite a brisk device, well able to spin its front wheels in the dry if you turn of the traction control, so it’s as well that the TTS gets four wheel drive, because it is obviously quicker still. This is very accessible power too, the strengthened balancer shaft four reaching peak torque at a low 2500rpm and staying there all the way to 5000rpm.

Such is its enthusiasm that at times you must deploy deft footwork to avoid jerking changes, an issue completely banished if you go for the S Tronic version. That fat torque spread makes it effortlessly easy to surge across the countryside, the all-wheel drive system heightening the Audi’s reassuring aura of stability.

However, tight bends in the wet can trouble it if you’re over-ambitious, with understeer setting in pretty determinedly, if briefly because the ESP soon quells it.

That’s a bit of a surprise given that the quattro’s Haldex clutch has scope to send as much 100 per cent of the available torque to either axle, and that it’s quicker to react now that it uses an electric rather than a hydraulic pump.

But it’s not quick enough if our experience on this tight, sodden bends was a guide, extra torque reaching the rear wheels only after you’ve gone in briskly, backed off, and re-applied the throttle, the TTS then sitting on its haunches to slingshot, quite impressively, out of the corner.

The TTS ride is firmer than you’ll experience in the standard car, and firmer still if you prod the sport button on the centre console, which stiffens the magnetic dampers to the point that the car bobs and jerks uncomfortably on motorways.

Also mighty impressive is the combination of performance and fuel consumption delivered by this engine. True, it has the advantage of less weight to push around, but the combination of a 5.5sec 0-62mph time and a combined consumption figure of 29.4 mpg (and CO2 emissions of 191g/km) is a real achievement.

The engine is pretty civilised too, but you won’t be hearing particularly tuneful sounds from it because it sounds rather flat despite those quad exhausts.